×

Propagation of analytic singularities up to non smooth boundary. (English) Zbl 0666.58043

Journ. Équ. Dériv. Partielles, St.-Jean-De-Monts 1987, Exp. No. 7, 9 p. (1987).
Let M be a real analytic manifold of dimension n, X be a complexification of M. \(\Omega\) be an open subset of M. The author gives the definition of a microsupport, which coincides with the classical analytical wave front set over \(\Omega\), but it may be strictly larger than its closure in \(T^*M\). Let P be a differential operator on X, u a hyperfunction on \(\Omega\) solution of the equation \(Pu=0\). Under some conditions on the principal symbol \(\sigma\) (p) it is proved that \(p\in SS_{\Omega}(u)\) implies \(b^+_ p\in SS_{\Omega}(u)\), where \(b^+_ p\) is the positive half integral curve of the real Hamiltonian vector field which corresponds to the function Im \(\sigma\) (p).
Reviewer: M.Novickij

MSC:

58J47 Propagation of singularities; initial value problems on manifolds
Full Text: Numdam EuDML